The universe is expanding. Light from distant galaxies is stretched red as it travels — cosmological redshift. Pick a redshift and see how far the light traveled, how long it took, and how old the universe was when it was emitted.
01Pick a redshiftscenario · observable epoch
Cosmic distances
Coma Cluster
A nearby cluster of ~1,000 galaxies, 320 million light-years away
Redshift z0.023
Scale factor a0.9775
Cosmic timeline · where this light was emitted
today
02Light travel timet_L = ∫ dz / [(1+z) H(z)]
Light traveled for
321 million yr
The Coma Cluster as we see it today is the Coma Cluster as it was 321 million years ago.
Recession velocity: 6,900 km/s — the cluster is receding at 2.3% the speed of light due to cosmic expansion.
Present-day proper distance to the object. Comoving means accounting for cosmic expansion since the light was emitted.
D_C = c ∫ dz/H(z)
Angular diameter distance
97.3 Mpc
Distance used for apparent size calculations. Counterintuitively, this peaks around z=1.6 and then DECREASES — far objects look bigger than nearer ones at very high z.
D_A = D_C / (1+z)
Luminosity distance
102 Mpc
Distance used for brightness calculations. The factor (1+z)² accounts for both light dilution and photon energy loss.
D_L = D_C × (1+z)
Hubble parameter H(z)
68.2 km/s/Mpc
Expansion rate at this redshift. Today H₀ = 67.4 km/s/Mpc. Was higher in the past — matter-dominated era had faster Hubble flow.
H(z) = H₀√[Ω_m(1+z)³ + ΩΛ]
Universe age at emission
13.46 Gyr
How old the cosmos was when this light started its journey. Subtract from 13.787 Gyr (today) to get the lookback time.
t(z) = 13.787 Gyr - t_L
CMB temperature then
2.79 K
Cosmic microwave background temperature at this redshift. Today: 2.725 K. At recombination (z=1090): ~3,000 K.